This work is a preliminary study on the use of the extended Kalman filter (EKF) for the state estimation of multibody systems. The observers based on the EKF are described by first-order differential equations, with independent, non-constrained coordinates. Therefore, it should be investigated how to formulate the equations of motion of the multibody systems so that efficient, robust and accurate observers can be derived, which can serve to develop advanced real-time applications. In the paper, two options are considered: a state-space reduction method and the penalty method. Both methods are tested on a four-bar mechanism with a linear spring-damper. The results enable us to analyze the pros and cons of each method and provide clues for future research.